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A is an n x n matrix. Check the true statements below: A. A number c is an eigenvalue of A if and only if the equation (A - cI)x= 0 has a nontrivial solution .. B. To find the eigenvalues of A, reduce chelon form. C. If Ax = Xx for some vector, then A is an eigenvalue of A. D. Finding an eigenvector of A might be difficult, but checking wheth given vector is in fact an eigenvector is easy. E. A matrix A is not invertible if and only if 0 is an eigenvalue of A.

A is an n x n matrix. Check the true statements below: A. A number c is an eigenvalue of A if and only if the equation (A - cI)x= 0 has a nontrivial solution .. B. To find the eigenvalues of A, reduce chelon form. C. If Ax = Xx for some vector, then A is an eigenvalue of A. D. Finding an eigenvector of A might be difficult, but checking wheth given vector is in fact an eigenvector is easy. E. A matrix A is not invertible if and only if 0 is an eigenvalue of A.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A is an \( n \times n \) matrix. Check the true statements below: - □ A. A number \( c \) is an eigenvalue of \( A \) if and only if the equation \( (A - cI)x = 0 \) has a nontrivial solution \( x \). - □ B. To find the eigenvalues of \( A \), reduce \( A \) to echelon form. - □ C. If \( Ax = \lambda x \) for some vector \( x \), then \( \lambda \) is an eigenvalue of \( A \). - □ D. Finding an eigenvector of \( A \) might be difficult, but checking whether a given vector is in fact an eigenvector is easy. - □ E. A matrix \( A \) is not invertible if and only if 0 is an eigenvalue of \( A \).
Transcribed Image Text:A is an \( n \times n \) matrix. Check the true statements below: - □ A. A number \( c \) is an eigenvalue of \( A \) if and only if the equation \( (A - cI)x = 0 \) has a nontrivial solution \( x \). - □ B. To find the eigenvalues of \( A \), reduce \( A \) to echelon form. - □ C. If \( Ax = \lambda x \) for some vector \( x \), then \( \lambda \) is an eigenvalue of \( A \). - □ D. Finding an eigenvector of \( A \) might be difficult, but checking whether a given vector is in fact an eigenvector is easy. - □ E. A matrix \( A \) is not invertible if and only if 0 is an eigenvalue of \( A \).
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